Remove selection overlays when Editing UVs?
You can get close (though you still need to keep Edit mode enabled):


In the 3D View's Properties region (N), go to the Display panel and enable the Only Render checkbox
In the Mesh Display panel, disable all of the overlays
Change to Edge Select mode in the 3D View (this at least hides the vertices, although the edges will still be highlighted).


And if you enable the UV Select Sync button in the UV editor (it's in the header), then the only edges you'll see in the 3D View are the ones that are selected in the UV editor.